Orthogonality of matrices in the Ky Fan $k$-norms

Abstract

We obtain necessary and sufficient conditions for a matrix $A$ to be Birkhoff-James orthogonal to another matrix $B$ in the Ky Fan $k$-norms. A characterization for $A$ to be Birkhoff-James orthogonal to any subspace $\mathcal{W}$ of $\mathbb{M}(n)$ is also obtained.

15 pages

References in corpus (1)

• Norm-parallelism in the geometry of Hilbert $C^{\ast }$-modules

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